:::#No, Fermat, Newton, Leibniz did not use tiny numbers: they used quantities which differed from numbers - and they used them with various degrees of discomfort.

:::#No, Fermat, Newton, Leibniz did not use tiny numbers: they used quantities which differed from numbers - and they used them with various degrees of discomfort.

:::#"infinitesimal" as a noun exists since the 1650s in the English language - but that is of not much relevance, as Newton published some of his work in Latin, and furthermore, used the term "moments" instead of "infinitesimals". In his later works, he tried to avoid infinitesimals.

:::#"infinitesimal" as a noun exists since the 1650s in the English language - but that is of not much relevance, as Newton published some of his work in Latin, and furthermore, used the term "moments" instead of "infinitesimals". In his later works, he tried to avoid infinitesimals.

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:::#No, Cauchy and Riemann got rid of infinitesimals, thereby putting the theory on sound footing. Abraham Robinson with his non-standard analysis infinitesimals rigorous - but this was in the 1960s

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:::#No, Cauchy and Riemann got rid of infinitesimals, thereby putting the theory on sound footing. Abraham Robinson with his non-standard analysis made infinitesimals rigorous - but this was in the 1960s

:::#This is all quite basic stuff. I should be surprised that someone who claims to be able to identify the greatest modern mathematician just by looking on a chart of published papers knows so little about the history of the mathematics (and the mathematicians) he is talking about. But this being Conservapedia, and the someone being you, the surprise is somewhat infinitesimal...

:::#This is all quite basic stuff. I should be surprised that someone who claims to be able to identify the greatest modern mathematician just by looking on a chart of published papers knows so little about the history of the mathematics (and the mathematicians) he is talking about. But this being Conservapedia, and the someone being you, the surprise is somewhat infinitesimal...

Latest revision as of 02:16, 31 July 2018

I'm not qualified to judge which it is, but it's been dealt with now. RDre 14:19, 11 April 2007 (EDT)

Good start, but ...

In the early 1600's Galileo began to show signs of a modern attitude toward the infinite, when he proposed that "infinity should obey a different arithmetic than finite numbers." But it was not until the late 19th century that Georg Cantor (1845-1918), a German mathematician, finally put infinity on a firm logical foundation and described a way to do arithmetic with infinite quantities useful to mathematics. [1]

Contents

Limit at the top of the page

Wow...Just wow...You guys claim that
is infinite. ...I don't know what to say to this. Any student who's had more than a week of calculus knows that this is incorrect. The correct statement is the limit from the right. The way you have it, the limit is undefined. Andy Schlafly, weren't you supposedly trained in a semi-technical field..? I'm amazed about the mistakes you make. Both here and on your "counterexamples to relativity" page....Wow... AndyFrankinson 20:02, 14 October 2011 (EDT)

Rough and sloppy

I need a lot of help with this article. It had a mention of division by zero, which all mathematicians (and most math students) know is a forbidden operation. Don't put nonsense like that in math articles. --Ed PoorTalk 10:47, 18 September 2009 (EDT)

I like your new edits. What else are you thinking of adding? I will help where I can. --MarkGall 11:35, 18 September 2009 (EDT)

My recent changes

I hope I have beaten the readers over the head sufficiently with the dictum that infinity is not a number, and hence dealt with Ed's complaint about this. You just don't divide by zero. Period. It's illegal. If you see an equation that appears to be dividing by zero, that equation is wrong.

I have taken out the stuff about "sample size". That refers to the size of a set in the field of statistics. We already cover set cardinality in general.

I have taken out the reference to "elementary techniques". That was meaningless, and seemed to be invoking the notion of "elementary proof", which is a page that needs a lot of work. Invoking that notion from here is just confusing the issue. Unless, of course, someone can clarify what that means, and give citations.

I can't figure out how to get spacing between the "math" parts and the "plain" parts in my list of 5 equations, so it looks horrible. Does anyone know how to do this? I know how in LaTeX, but that's way too complicated for a wiki, and probably wouldn't work.

My concept of infinity

To me, the only infinity is that in which God has lived before creating us, and that which He grants us in Heaven. That's all I have to say about it. --Pious (talk) 00:47, 20 April 2017 (EDT)

Were the Greeks flat out wrong?

This page seems to go at the Greeks in a biased way. It says they were "flat out wrong" about infinity -- even if this is correct, I think this sentence certainly needs re-phrasing. Anyways, while I think that God is certainly infinite, I do not accept that infinity can exist in the natural world, and so I consider that the Greeks were, to some extent, correct. Philosophers are generally in agreement with me as well.

Definition

Merriam-Webster's definition of infinity is unusually inadequate: "an indefinitely great number or amount." The essence of infinity is not that it is indefinite.--Andy Schlafly (talk) 00:36, 18 May 2018 (EDT)

Bernhard Riemann

Inherent in the concept of infinity is the concept of infinitesimal: infinity small. Bernhard Riemann identified the sum of infinitesimal strips of area under a function to establish a rigorous definition of the integral, now known as the Riemann Integral.

I think that this misrepresents Bernhard Riemann's ideas:

The infinitesimals were tools of the creative geniuses of the 18th century, as Euler, Leibniz, and Newton. Riemann took a step away: he does not talk about things which are infinitely small, but which become infinitely small - using the idea of limits. Therefore, the integral is not the sum of infinitesimal strips, but the limit of finite sums of small stripes, becoming smaller and smaller.

That may sound like hair-splitting, but his approach could be rigorously formalized quite easily, while this was much more difficult for infinitesimals.--AugustO (talk) 10:36, 30 July 2018 (EDT)

Not sure if there is a meaningful distinction here. Infinitely small is inherently a limit. But you make a very interesting point and I'll think about it further. Also, did Euler, Leibniz or Newton use the concept of infinitesimal?--Andy Schlafly (talk) 12:24, 30 July 2018 (EDT)

Fermat had already used infinitesimals to calculate the tangents of polynomials. For the parabola y=, he would look at the secant through the points (x,), (x+D,) which are separated at the x-axis by the infinitesimal distance and then calculate Calculations like this drove philosophers like Hobbes crazy: how can you say something is zero at one time and works not as zero another time. For us, it is easy to reconcile this by introducing limits, but those were not thought of for quite a while!

Euler used infinitesimals creatively, Leibniz called them etc. If I recall correctly, Newton did not generally use them for integration: he transformed the function which he wanted to integrate into a power series, integrated the parts of the series (as it was well known how to integrate polynomials), and at last, tried to transform the resulting power-series back into a well-known function. The first and the third step often required quite an ingenuity

In my opinion one of the great things about Riemann-Cauchy-integration is that it transformed an art into a craft: only few had the talent to use infinitesimals in a way that provided correct results!

That's fascinating history, August! Sounds like Fermat et al. used tiny numbers, but Cauchy and Riemann made it infinitesimal rigorous. Note that Merriam-Webster says the term infinitesimal did not exist in English until the early 1700s, which would have been late in the game for Newton.--Andy Schlafly (talk) 00:15, 31 July 2018 (EDT)

No, Fermat, Newton, Leibniz did not use tiny numbers: they used quantities which differed from numbers - and they used them with various degrees of discomfort.

"infinitesimal" as a noun exists since the 1650s in the English language - but that is of not much relevance, as Newton published some of his work in Latin, and furthermore, used the term "moments" instead of "infinitesimals". In his later works, he tried to avoid infinitesimals.

No, Cauchy and Riemann got rid of infinitesimals, thereby putting the theory on sound footing. Abraham Robinson with his non-standard analysis made infinitesimals rigorous - but this was in the 1960s

This is all quite basic stuff. I should be surprised that someone who claims to be able to identify the greatest modern mathematician just by looking on a chart of published papers knows so little about the history of the mathematics (and the mathematicians) he is talking about. But this being Conservapedia, and the someone being you, the surprise is somewhat infinitesimal...